Effective field theories for gapless phases with fractons via a coset construction

TL;DR

This paper develops a symmetry-based effective field theory for gapless phases with fractonic defects, using a coset construction that reproduces elasticity theories and incorporates topological defects, revealing their fractonic origin.

Contribution

It introduces a coset construction approach to derive effective field theories for fractonic phases, connecting symmetry breaking, topological defects, and elasticity theories.

Findings

Reproduces classical elasticity as a low-energy limit

Incorporates topological defects like dislocations and disclinations

Identifies Wess-Zumino terms affecting quasiparticle scattering

Abstract

Fractons are particles with restricted mobility. We give a symmetry-based derivation of effective field theories of gapless phases with fractonic topological defects, such as solids and supersolids, using a coset construction. The resulting theory is identified as the Cosserat elasticity theory, which reproduces the conventional symmetric elasticity theory at low energies. The construction can be viewed as a dynamical realization of the inverse Higgs mechanism. We incorporate topological defects such as dislocations and disclinations, which are nontrivially related by the Bianchi identities of defect gauge fields. The origin of the fractonic nature of defects in those systems can be traced back to the semidirect product structure of translational and rotational groups. The construction is immediately extendable to higher dimensions and systems with broken translational symmetries, such as solids, supersolids, and vortex crystals. We identify Wess-Zumino terms in supersolids, which induce quasiparticle scatterings on topological defects.